First and foremost, this patch implements the latest best practices in C++ (i.e. comparison operators are not member functions).
The main objective of this rewrite is to have these operators callable in slightly more general contexts (*this->asFontTag() == *rhs.asFontTag() yielded an error because no member function could be called). This feature is no more required.
The rewrite took place in the context of https://www.lyx.org/trac/ticket/12585. The first iteration was using more complex code to circumvent XMLStream in DocBook (see details in the bug above and in the mailing list), while this one uses XMLStream fully. The bug was due to font tags being considered equal when they were not, due to the comparison done only on the XML tag and not on the actual font change (XML attributes can complement the tag for various font changes).